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Simplifying v2 + -8v + -6 = 0 Reorder the terms: -6 + -8v + v2 = 0 Solving -6 + -8v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -8v + 6 + v2 = 0 + 6 Reorder the terms: -6 + 6 + -8v + v2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -8v + v2 = 0 + 6 -8v + v2 = 0 + 6 Combine like terms: 0 + 6 = 6 -8v + v2 = 6 The v term is -8v. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8v + 16 + v2 = 6 + 16 Reorder the terms: 16 + -8v + v2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + -8v + v2 = 22 Factor a perfect square on the left side: (v + -4)(v + -4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (v + -4) equal to 4.69041576 and -4.69041576.Subproblem 1
v + -4 = 4.69041576 Simplifying v + -4 = 4.69041576 Reorder the terms: -4 + v = 4.69041576 Solving -4 + v = 4.69041576 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = 4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + v = 4.69041576 + 4 v = 4.69041576 + 4 Combine like terms: 4.69041576 + 4 = 8.69041576 v = 8.69041576 Simplifying v = 8.69041576Subproblem 2
v + -4 = -4.69041576 Simplifying v + -4 = -4.69041576 Reorder the terms: -4 + v = -4.69041576 Solving -4 + v = -4.69041576 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = -4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + v = -4.69041576 + 4 v = -4.69041576 + 4 Combine like terms: -4.69041576 + 4 = -0.69041576 v = -0.69041576 Simplifying v = -0.69041576Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.69041576, -0.69041576}
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